There is a tank with 100L of water where 4kg of salt is dissolved. You open a faucet to add a salt solution of .6kg/L at the constant speed of 10 L/min. When do you have to close the faucet if you want the concentration of the salt solution in the tank to be .25kg/L in the tank? Find the time it takes after the faucet is open to the nearest minute.

a) The direct variation equation is y = 33x.

b) The customer can pay the company to collect 15 bins.

c) The customer can get approximately 16 bins (rounded to the nearest whole number) removed for $500 with a $30 tip included.

A) The direct variation equation to represent the cost would be y = kx, where y represents the cost, x represents the number of bins collected, and k is the constant of proportionality. In this case, since the cost is $33 for each bin collected, the value of k is 33. Therefore, the direct variation equation is y = 33x.

B) To find the number of bins a customer can pay the company to collect for $500, we can set the cost (y) equal to $500 and solve for x (the number of bins). Thus, we have:

y = 33x

500 = 33x

x = 500/33

x ≈ 15.15

Therefore, the customer can pay the company to collect 15 bins (rounded to the nearest whole number) for $500.

C) If the customer plans to tip the recycling company $30, the total cost would be $500 + $30 = $530. We can set the cost (y) equal to $530 and solve for x:

y = 33x + 30

530 = 33x + 30

500 = 33x

x ≈ 15.91

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The solution of the given logarithm function log(f-3)-log(17-40) is

f < 3.

So no option is correct.

A logarithm function is a mathematical function that describes the relationship between a given number (called the argument or input) and a specified base. The logarithm of a number x with respect to a base b is the power to which b must be raised to give x.

In other words, if we have the equation y = log_b(x), then y represents the power to which the base b must be raised to get x. For example, if b=2, then log_2(8) = 3 because 2 raised to the power of 3 equals 8.

The given expression is:

log(f-3)-log(17-40)

We can simplify this expression using the property of logarithms:

log(a) - log(b) = log(a/b)

So, we get:

log((f-3)/(17-40))

Now, for this expression to have a real solution, the argument of the logarithm must be positive, so we have:

(f-3)/(17-40) > 0

Solving for f, we get:

f - 3 < 0 (since 17-40 is negative)

f < 3

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Answer:

2800=1.4tons

Step-by-step explanation:

2000Ib=1ton

Where is the question?

The solution of the system of equations is given by the point of intersection of all the equations that compose the graph.

In this problem, the graph of the system of equations is given, hence we use it to obtain the solution.

The solution of the system of equations is given by the point of intersection of all the equations that compose the graph, that is, the point where all the curves cross each other.

The point of intersection represents the solution of the system of equations as it is the input values for which all the equations have the same output value.

The problem is incomplete, hence the procedure to obtain the solution of the system of equations from the graph is presented.

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Answer:

-----------------------

Tangent line is perpendicular to radius at the point of tangency.

Hence we have:

Therefore ΔMKJ is a right  triangle.

Radius is 11, so diameter is 22, this is one of legs and its hypotenuse is 25 units.

Use Pythagorean theorem to find the missing leg:

A function with a vertex must switch from increasing to decreasing or vice versa at the vertex. So, the function cannot be only increasing or only decreasing over its entire domain.

Given data ,

A function with a vertex, also known as a vertex form of a quadratic function, is a function of the form f(x) = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. The vertex is the point on the parabola where it changes direction from increasing to decreasing or vice versa.

It is impossible for a function with a vertex to increase continuously if its whole domain shows an increase in the function. Similar to the last example, a function with a vertex cannot decrease throughout its whole domain because that would imply that the function is constantly decreasing.

Hence , a function with a vertex must switch from increasing to decreasing or vice versa at the vertex, and it cannot be only increasing or only decreasing over its entire domain.

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Time Series Graph: Plot A

Based on the above plot, earnings first rise till 1997, and then start falling till 2001. After 2001, earnings start rising again. So overall there is an upward trend.

Based on these observations, the answer is Option A, which says:

Option A: There is a general upward trend though there have benn some down years. An upward trend would be helpful to women so that their earnings become equal to those of men.

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Answer:

3cm

Step-by-step explanation:

triangle formula is height times base divided by two and divide base by two. then its 6 and divide 6 from 18. so the answer is 3cm

Simplifying the expression √y⁶ for y is y³

From the question, we have the following parameters that can be used in our computation:

sqrt y^6

Rewrite the expression using numbers and mathematical symbol

So, we have

√y⁶

Take the square root of both sides

So, we have

√y⁶ =  y³

Hence, the solution to the expression √y⁶ is  y³

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Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year

Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit

Depreciation rate = 2 / 3 = 0.667 or 66.7%

Method of the straight line:

Annual depreciation = (Cost - Residual value) / Useful life

Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year

Schedule of depreciation: shown in the below table

Units-of-production method:

Depreciation per unit = (Cost - Residual value) / Total units of production

Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit

Depreciation schedule:

Double-declining-balance method:

Depreciation rate = 2 / Useful life

Depreciation rate = 2 / 3 = 0.667 or 66.7%

Depreciation schedule: shown in the below table

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True, option (G) is which is - at least one of the numbers is positive.

A positive integer is a whole number greater than zero, i.e., any number that can be expressed without fractions or decimals, and is greater than zero.

If the difference of two numbers is less than the sum of the numbers, it is always true that at least one of the numbers is positive. As a result, "At least one of the numbers is positive" is the response, which is (G).

Here we assume that x and y are two numbers. The difference between the two numbers is |x - y|, which is always positive.

Now, according to the given condition:

|x - y| < x + y

Simplifying this inequality, we get:

-x + y < x + y

2y > 0

Dividing both sides by 2, we get:

y > 0

Therefore, we can conclude that at least one of the numbers (y) is positive. Note that it is possible for both numbers to be positive or for one number to be positive and the other to be zero.

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Answer:

Step-by-step explanation:

To find the point at which the two plans cost the same, we can set their total costs equal to each other:

55 + 0.13x = 48 + 0.15x

Simplifying and solving for x, we get:

0.02x = 7

x = 350

Therefore, the plans will cost the same when Lisa drives 350 miles.

To find the cost at this point, we can substitute x=350 into either equation. Let's use the first plan:

Total cost = 55 + 0.13(350) = $97.50

Therefore, if Lisa drives 350 miles, the cost for either plan will be $97.50.

Considering both functions, there are no restrictions or exclusions for any real number values in the domain. Therefore, the domain of the composition (f∘g)(x) is all real numbers.

To determine the domain of the composition (f∘g)(x), we need to consider the domains of both functions f(x) and g(x) and determine any restrictions.

The function f(x) =[tex]1x + 2[/tex] does not have any explicit restrictions on its domain. It is defined for all real numbers.

The function g(x) = [tex]x^2 - 2x[/tex] is a quadratic function. Quadratic functions are defined for all real numbers, so there are no restrictions on the domain of g(x).

When we compose functions, we need to ensure that the output of the inner function is within the domain of the outer function. In this case, the composition (f∘g)(x) means we substitute g(x) into f(x), resulting in f(g(x)).

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The regression equation that fits the scenario will be y = 11.46 e1.107x

Utilizing this method with the provided information, we attain the regression equation:

ln y = 2.4502 + 0.0515x

It should be noted that to find the exponential equation, we can elevate both sides of the equation:

y = e^(2.4502 + 0.0515x) = 11.46 * e^(1.107x)

Consequently, the mathematical model that is most suitable for the mentioned data is:

y = 11.46 * e^(1.107x)

The coefficient of determination (R-squared) for said model is 0.994, thus indicating an incredibly strong fit.

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the probability of a major tornado in three consecutive years is 1/8000.   the probability of not having a major tornado in the next ten years is approximately 0.328. he probability of having at least one major tornado in the next ten years is approximately 0.672.

(a) The probability of a major tornado in any single year is 1/20. To find the probability of a major tornado in three consecutive years, we multiply the probabilities together:

P(major tornado in 3 consecutive years) = (1/20) * (1/20) * (1/20) = 1/8000

So the probability of a major tornado in three consecutive years is 1/8000.

(b) The probability of not having a major tornado in any single year is 19/20. To find the probability of not having a major tornado in the next ten years, we raise this probability to the power of 10:

P(no major tornado in next 10 years) = (19/20)^10 ≈ 0.328

So the probability of not having a major tornado in the next ten years is approximately 0.328.

(c) To find the probability of having at least one major tornado in the next ten years, we can subtract the probability of having no major tornadoes in the next ten years from 1:

P(at least one major tornado in next 10 years) = 1 - P(no major tornado in next 10 years)

P(at least one major tornado in next 10 years) = 1 - (19/20)^10 ≈ 0.672

So the probability of having at least one major tornado in the next ten years is approximately 0.672.

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The error made by Tony is in Step 4, where he wrote "x + 2 = ± 81". The correct step should be:

Step 4: Take the square root of both sides to solve for x.

√((x + 2)^2) = √81

In this step, Tony should have taken the square root of both sides, but he made the mistake of only taking the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.

The correct step should be:

x + 2 = ±9

Step 5: Solve for x.

x + 2 = 9 or x + 2 = -9

Step 6: Subtract 2 from both sides to isolate x.

x = 9 - 2 or x = -9 - 2

This will give the correct solutions:

x = 7 or x = -11

So, the error made by Tony occurred in Step 4 where he only took the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.

Hope this helps!

Answer:

Let the three numbers be x, y, and z.

We are given that x + y = z + 4.

We are also given that x + y + z >= 20 and x + y + z <= 28.

Combining these two inequalities, we get:

z + 4 + z >= 20

2z >= 16

z >= 8

Since z is an integer, z can be 8, 9, 10, 11, 12, 13, 14, 15, 16, or 17.

For each value of z, we can find the corresponding values of x and y using the equation x + y = z + 4.

For example, if z = 8, then x + y = 12.

So, the three integral values satisfying the inequality are 8, 4, and 0.

Another example is z = 15.

In this case, x + y = 19.

So, the three integral values satisfying the inequality are 15, 2, and 2.

There are many other possible solutions.

Answer:

C

Step-by-step explanation:

The theoretical probability of landing on A, B, C, or D is all 1/4. This would also mean the theoretical probability is 45/180. Statement C is the only one that is true.

angle 1 = 180 - 74 the angle on a straight line is given as 180

= 106 degrees

Alternate angles are a pair of angles formed by a transversal intersecting two parallel lines. These angles are located on opposite sides of the transversal and on opposite sides of the parallel lines.

The alternate angles are congruent, which means they have the same measure or degree. In other words, if one alternate angle measures x degrees, then its corresponding alternate angle will also measure x degrees.

angle 2 = angle 1

They are vertical angles hence they are equal

angle 3 = 74 degrees

They are  vertical angles as well

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Answer:

Step-by-step explanation:

y = 5x^3 - x

Slope of a secant

= (y2 - y1)/(x2-x1)     where (x1, y1) and (x2, y2) are the 2 points.

Slope for the interval (1, 2)

= [5(2)^3 - 2)- (5(1)^3 - 1)] / (2-1)

= 34

Slope for interval (1, 1.5)

=  [5(1.5)^3 - 1.5)- (5(1)^3 - 1)] / (1.5-1)

= 22.75

In the same way we get the slopes of the  intervals:

(1, 1.1):-  15.55

(1, 1,01):-  15.15

(1, 1.001):- 15.015

So the answer is 15.

We can actually see here that the equation for the population P in terms of time t in minutes will be: P = 404 × 2^(t/36).

We can see here that looking at the change in population, we can use the following:

P = P₀ × 2^(t/Δt).

Where:

P₀ = initial population = 404 bacterias

t = time elapsed (in minutes).

Δt = time it takes for the population to double (36 minutes).

Thus, we see that substituting this, we have:

P = 404 × 2^(t/36).

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its c please mark me as a brainliest

the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students,

How to solve the problem?

Let's use the following variables to represent the unknowns in the problem:

Let A be the area of area A

Let B be the area of area B

Let x be the number of students working in area B in the morning

Let 3x be the number of students working in area A in the morning

Let y be the total number of students in the group

From the problem statement, we know that A = 1.5B (since area A is 1.5 times area B). We also know that in the morning, the number of students working in area A is 3 times the number of students working in area B. This can be expressed as:

3x = y/2 (since half of the students work in the morning)

In the afternoon, 7/12 of the students work in area A, so the number of students working in area B is:

(1-7/12)y = 5/12y

At the end of the day, area A is done and area B still needs 4 more students to work for another day. This means that the amount of work done by the students in area B is (y/2 - 3x) + (5/12y - 4B) = B, since the total work needed to be done in area B is B and the amount of work done by the students in area A is y/2 - 3x.

Substituting A = 1.5B and 3x = y/2, we can solve for y:

(y/2 - 3x) + (5/12y - 4B) = B

y/2 - 3(y/2)/3 + 5/12y - 4B = B

y/2 - y/2 + 5/12y = 5B

17/12y = 5B

y = (5/17)12B

Therefore, the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students, but we can say that the number of students is proportional to the area of area B. If we know the area of area B, we can use the equation above to find the total number of students in the group.

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An expression in factored form for the polynomial of least possible degree is y(x) = (x-2)(x+2).

What is polynomial?

Polynomials can be represented in various forms, including standard form, factored form, and expanded form. Standard form is where the polynomial is written with the terms in descending order of degree, with coefficients in front of each term. Factored form is where the polynomial is written as a product of linear factors, and expanded form is where the polynomial is written out in full, with all the terms multiplied together.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using addition, subtraction, and multiplication operations. The variables are raised to non-negative integer powers, and the highest power of the variable is called the degree of the polynomial.

For example, the polynomial 2x³ + 3x³ - 4x + 1 has degree 3, as the highest power of x is 3. The coefficients in this polynomial are 2, 3, -4, and 1.

Here, the curve touch two points (-2,0) and (2,0).

So, we can say (-2) and 2 are the root of the polynomial.

We know of a and b are two root of any polynomial then the polynomial will be (x-a)(x-b).

So, the expression is y(x) = (x-2)(x+2).

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The equation of this graphed line is equal to y = x/2 - 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 + 5)/(8 - 0)

Slope (m) = 4/8

Slope (m) = 1/2.

At data point (0, -5) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = 1/2(x - 0)

y + 5 = x/2

y = x/2 - 5

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Option C) EG bisects ZFEH would prove that EFGH is a square.

In geometry, a quadrilateral is a polygon with four sides and four vertices (corners). It is a two-dimensional shape with four straight sides, and the sum of its interior angles is equal to 360 degrees. Some common types of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. Each type of quadrilateral has its own unique set of properties, such as congruent sides and angles, parallel sides, or perpendicular diagonals. Quadrilaterals are used in many areas of mathematics, as well as in engineering, architecture, and other fields.

Here,

A rhombus has opposite sides congruent, but its angles are not necessarily right angles. However, if the diagonals of a rhombus are perpendicular bisectors of each other, then the rhombus is a square.

If EG bisects ZFEH, then the opposite angles of the rhombus are congruent and the diagonals of the rhombus are perpendicular bisectors of each other. This means that EFGH is a square, and all its sides and angles are congruent.

Options A), B), and D) do not provide any information about the shape of EFGH.

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